I totally understand everything that you're going through! And, if it helps, I think that it's completely normal, but talking to the HV will help you out with this, I promise!
I feel the same, emotional way with my little girl, she's 4 months old now and I still get really sad because I think that I can't do this and that and the other. I think that it might really help you to focus on the great things that you manage to offer your baby. You still manage to feed her, give her a roof over her head, she has clothes on her back, etc. I keep having to remind myself that this is a really emotional time for any Mother and it's okay to cry.
No one can tell you how to parent your child, you're thinking of your baby as the number one priority and that's what you need to do. You are her Mother and it sounds like you're doing a great job! This step Father-in-law person sounds like he isn't thinking of your baby as the number one in this situation, so try not to let his opinions have too much of an affect on you. I know that it's easier said than done, but you have the final say and he doesn't.
In regards to your partner, staying out until 6am without telling you and answering the phone is a major nob head move. I mean, maybe he is just feeling really overwhelmed with his home life situation too, and he has the luxury of being able to stay out all night. I know that people deal with stress in different ways, but it sounds like he is going about it the wrong way. I've been in a very similar situation with my partner and, as I am pretty financially dependent on him too, I have learnt to just bite my tongue and focus all of my energy on my baby. Since I started doing that and laying into him less, he has started to open up to me a bit more and stay out less. But, the point is, that I don't waste my energy on thinking about it anymore. He is third, or forth, if you count the dog... down my list of priorities now!
I understand that it's hard and that you feel like you're doing it all by yourself sometimes.
Oh! Also, with your anxious thoughts about your baby, I read somewhere not long ago that over half of new mums have these horrible thoughts, so you are totally not alone in that!
I would recommend talking to your favourite HV, because they will have heard all of this before. And feel free to PM me, if you need to talk!